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An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first ...
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal.
1 Examples and types of graphs. 2 Graph coloring. ... This is a list of graph theory topics, ... Adjacency list; Adjacency matrix.
Simple graphs: Graphs without self-loops or multi-edges. Multi-edge graphs: Graphs allowing multiple edges between the same pair of nodes. Loopy graphs: Graphs that include self-loops (edges connecting a node to itself). Directed graphs: Models with specified in-degrees and out-degrees for each node.
In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge.The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v.
For each vertex we store the list of adjacencies (out-edges) in order of the planarity of the graph (for example, clockwise with respect to the graph's embedding). We then initialize a counter = + and begin a Depth-First Traversal from . During this traversal, the adjacency list of each vertex is visited from left-to-right as needed.
From the handshaking lemma, a k-regular graph with odd k has an even number of vertices. A theorem by Nash-Williams says that every k ‑regular graph on 2k + 1 vertices has a Hamiltonian cycle. Let A be the adjacency matrix of a graph. Then the graph is regular if and only if = (, …,) is an eigenvector of A. [2]
In mathematics, in graph theory, the Seidel adjacency matrix of a simple undirected graph G is a symmetric matrix with a row and column for each vertex, having 0 on the diagonal, −1 for positions whose rows and columns correspond to adjacent vertices, and +1 for positions corresponding to non-adjacent vertices.